Cycles Gradient between two materials
Here is one option to use the Vertex Paint Blur tool on the border between the white color vertex and the black color vertex. I paint the center area white in vertex paint mode, and then invert and set paint to black (in the header, go to Paint> Set Vertex Color and this will act like a fill). I used Face Select masking to do this without overriding the center white area. 


I then switch tools to the Blur tool and blur the area around the white spot so that it cause a gray area. To deepen it, I subdivide once to force the vertex paint to blend across the changes. I then use this vertex color in the Attribute node (named Col by default) as a factor to mix between a diffuse black shader and a blue emission shader.